Question #e6979

2 Answers
Feb 16, 2018

#d/dx{sinx+cosx}=d/dx{sinx}+d/dx{cosx}=cosx-sinx#.

Feb 16, 2018

#cos(x)-sin(x)#

Explanation:

#d/dx(sin(x)+cos(x))#

An important rule to know is that

#d/dx(x+y)=d/dx(x)+d/dx(y)#

The derivative of #sin(x)# is #cos(x)#, while the derivative of #cos(x)# is #-sin(x)#.

#:.d/dx(sin(x)+cos(x))=d/dx(sin(x))+d/dx(cos(x))#

#=cos(x)-sin(x)#

Source:

http://www.sosmath.com/calculus/diff/der03/der03.html